The Simplex Method: Nonstandard Problems

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Section 4.3

• The Simplex Method Nonstandard Problems

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Ex. A nonstandard maximization problem
Maximize P 8x 3y
Subject to
First change the inequalities to less than or
equal to.
Now proceed with the simplex method
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Introduce slack variables to make equations out
of the inequalities and set the objective
function 0
The initial tableau and notice v 2 (not
feasible)
We need to pivot to a feasible solution
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Ratios 8 2
Locate any negative number in the constant column
( 2). Now go to the first negative to the
left of that constant (1). This determines the
pivot column. The pivot row is found by
examining the positive ratios. So 1 is our
pivot.
Create unit column
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Note now we have a feasible solution proceed
with simplex
New pivot since it is the only positive ratio
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This is the final tableau x 2, y 4, P 28
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The Simplex Method for Nonstandard Problems

1. If necessary, rewrite as a maximization problem.
2. If necessary, rewrite inequalities as less or
   equal to.
3. Introduce slack variables and write simplex
   tableau.
4. If no negative constants (upper column) use
   simplex method, otherwise go to step 5.
5. Pick a negative entry in a row with a negative
   constant (this is the pivot column). Compute
   positive ratios to determine pivot row. Then
   pivot and return to step 4.